Answer: 5
Step-by-step explanation:
5 multiples by itself 4 times is 625.
5 x 5 x 5 x 5
Given polynomial 
.
(a) To show that (x – 3) is a factor of f(x).
Factor theorem:
<em>A polynomial f(x) has a factor of (x – a), if and only if f(a) = 0.</em>
= 0
f(3) = 0
Hence (x – 3) is a factor of f(x).
(b) 
Here 
is common in first 2 terms and 2 is common in next 2 terms.
Now, (x – 3) is common in both terms.
and 
x = 3 and 
3 is the real root.
using quadratic formula solve and find the other roots.
These are complex roots.
Hence 3 is the only real root of the equation f(x) = 0.
Answer:
log₁₀(10³) + log₁₀(10⁴)
= log₁₀( 10³ × 10⁴ )
= log₁₀( 10³⁺⁴)
= log₁₀( 10⁷)
Step-by-step explanation:
Given:
log₁₀(10³) + log₁₀(10⁴) = log₁₀(10⁷)
Now,
we know the property of log function that
log(A) + log(B) = log(AB)
therefore,
applying the above property on the LHS, we get
log₁₀(10³) + log₁₀(10⁴) = log₁₀( 10³ × 10⁴ )
also,
xᵃ + xᵇ = xᵃ⁺ᵇ
therefore,
log₁₀( 10³ × 10⁴ ) = log₁₀( 10³⁺⁴)
= log₁₀( 10⁷)
Hence,
LHS = RHS
Hence proved
I believe is -5 the right answer
